In this paper we present a fuzzy approach to the Reed-Frost model for epidemic spreading taking into account uncertainties in the diagnostic of the infection. The heterogeneities in the infected group is based on the clinical signals of the individuals (symptoms, laboratorial exams, medical findings, etc.), which are incorporated to the dynamic of the epidemic. The infectivity level is time-varying and the classification of the individuals is performed through fuzzy relations. Simulations considering a real problem data of the influenza epidemic in the baby daycare are performed and the results are compared with a stochastic Reed-Frost generalization developed by the authors in a previous work.